IRIS RECOGNITION BASED ON HILBERT–HUANG TRANSFORM 1 ...

Advances in Adaptive Data Analysis
Vol. 1, No. 4 (2009) 623–641
c○ World Scientific Publishing Company
IRIS RECOGNITION BASED ON
HILBERT–HUANG TRANSFORM
ZHIJING YANG∗ , ZHIHUA YANG † and LIHUA YANG∗,‡ ∗School of Mathematics and Computing Science
Sun Yat-sen University, Guangzhou 510275, China
† Information Science School
GuangDong University of Business Studies
Guangzhou 510320, China
‡ mcsylh@mail.sysu.edu.cn
As a reliable approach for human identification, iris recognition has received increasing
attention in recent years. This paper proposes a new analysis method for iris recognition
based on Hilbert–Huang transform (HHT). We first divide a normalized iris image into
several subregions. Then the main frequency center information based on HHT of each
subregion is employed to form the feature vector. The proposed iris recognition method
has nice properties, such as translation invariance, scale invariance, rotation invariance,
illumination invariance and robustness to high frequency noise. Moreover, the experimental
results on the CASIA iris database which is the largest publicly available iris
image data sets show that the performance of the proposed method is encouraging and
comparable to the best iris recognition algorithm found in the current literature.
Keywords: Iris recognition; empirical mode decomposition (EMD); Hilbert–Huang transform
(HHT); main frequency center.
1. Introduction
With increasing demands in automated personal identification, biometric authentication
has been receiving extensive attention over the last decade. Biometrics
employs various physiological or behavioral characteristics, such as fingerprints,
face, iris, retina and palmprints, etc., to accurately identify each individual. 13,29
Among these biometric techniques, iris recognition is tested as one of the most
accurate manner of personal identification. 4,6,14,22,23
The human iris, a thin circular diaphragm lying between the cornea and the lens,
has an intricate structure and provides many minute characteristics such as furrows,
freckles, crypts, and coronas. 2 These visible characteristics, which are generally
called the texture of the iris, are unique to each subject. 6,7,14,24 The iris patterns of
the two eyes of an individual or those of identical twins are completely independent
and uncorrelated. Additionally, the iris is highly stable over a person’s lifetime
and lends itself to noninvasive identification since it is an externally visible internal
623

624 Z.Yang,Z.Yang&L.Yang
organ. All these desirable properties make iris recognition suitable for highly reliable
personal identification.
For the last decade, a number of researchers have worked on iris recognition and
have achieved great progress. According to the various feature extractions, existing
iris recognition methods can be roughly divided into four major categories: the
phase-based methods, 6,7,23 the zero-crossing representation-based methods, 4,22 the
texture analysis-based methods 14,24 and intensity variation analysis methods. 15,16
A phase-based method is a process of phase demodulation. Daugman 6,7 made use
of multiscale Gabor filters to demodulate texture phase structure information of
the iris. Then the filter outputs were quantized to generate a 2048-bit iriscode
to describe an iris. Tisse et al. 23 encoded the instantaneous phase and emergent
frequency with the analytic image (two-dimensional Hilbert transform) as iris features.
The zero-crossings of wavelet transform provide meaningful information of
image structures. Boles and Boashash 4 calculated zero-crossing representation of
one-dimensional wavelet transform at various resolution levels of a virtual circle on
an iris image to characterize the texture of the iris. Wildes et al. 24 represented the
iris texture with a Laplacian pyramid constructed with four different resolution levels.
Tan et al. 14 proposed a well-known texture analysis method by capturing both
global and local details from an iris with the Gabor filters at different scales and
orientations. As an intensity variation analysis method, Tan et al. constructed a set
of one-dimensional intensity signals to contain the most important local variations
of the original two-dimensional iris image. Then the Gaussian–Hermite moments of
such intensity signals are used as distinguishing features. 16
Fourier and Wavelet descriptors have been used as powerful tools for feature
extraction which is a crucial processing step for pattern recognition. However, the
main drawback of those methods is that their basis functions are fixed and do not
necessarily match the varying nature of signals. Hilbert–Huang transform (HHT)
developed by Huang et al. is a new analysis method for nonlinear and nonstationary
data. 11 It can adaptively decompose any complicated data set into a finite
number of intrinsic mode functions (IMFs) that become the bases representing the
data by empirical mode decomposition (EMD). With Hilbert transform, the IMFs
yield instantaneous frequencies as functions of time. The final presentation of the
results is a time–frequency–energy distribution, designated as the Hilbert spectrum
that gives sharp identifications of salient information. Therefore, it brings not
only high decomposition efficiency but also sharp frequency and time localizations.
Recently, the HHT has received more attention in terms of interpretations 9,18,21 and
applications. Its applications have spread from ocean science, 10 biomedicine, 12,20
speech signal processing, 25 image processing, 3 pattern recognition 19,26,28 and
so on. Recently, EMD is also used for iris recognition as a low pass filter
in Ref. 5.
Since a random iris pattern can be seen as a texture, many well-developed texture
analysis methods have been adapted to recognize the iris. 14,24 An iris consists
of some basic elements which are similar to each other and interlaced each other,

Iris image preprocessing
Iris image Localization
Normalization
Iris Recognition Based on Hilbert–Huang Transform 625
Feature
extraction Classification
HHT LDA
Fig. 1. Diagram of the proposed method.
Output
i.e. an iris image is generally periodical to some extent. Therefore the approximate
period is an effective feature for the iris recognition. By employing the main frequency
center presented in our previous works 26,27 of the Hilbert marginal spectrum
as an approximation for the period of an iris image, a new iris recognition method
based on HHT is proposed in this paper. Unlike directly using the residue of the
EMD decomposed iris image for recognition in Ref. 5, the proposed method utilizes
the main frequency center information as the feature vector which is particularly
rotation invariant. In comparison with the existing iris recognition methods, the
proposed algorithm has an excellent percentage of correct classification, and possesses
very nice properties, such as translation invariance, scale invariance, rotation
invariance, illumination invariance and robustness to high frequency noise. Figure 1
illustrates the main steps of our method.
The remainder of this paper is organized as follows. Brief descriptions of image
preprocessing are provided in Sec. 2. A new feature extraction method and matching
are given in Sec. 3. Experimental results and discussions are reported in Sec. 4.
Finally, conclusions of this paper are summarized in Sec. 5.
2. Iris Image Preprocessing
An iris image, contains not only the iris but also some irrelevant parts (e.g. eyelid,
pupil, etc.). A change in the camera-to-eye distance may also result in variations in
the size of the same iris. Therefore, before feature extraction, an iris image needs
to be preprocessed to localize and normalize. Since a full description of the preprocessing
method is beyond the scope of this paper, such preprocessing is introduced
briefly as follows.
The iris is an annular part between the pupil (inner boundary) and the sclera
(outer boundary). Both the inner boundary and the outer boundary of a typical iris
can approximately be taken as circles. This step detects the inner boundary and
the outer boundary of the iris. Since the localization method proposed in Ref. 14 is
a very effective method, we adopt it here. The main steps are briefly introduced as
follows. Since the pupil is generally darker than its surroundings and its boundary
is a distinct edge feature, it can be found by using edge detection (Canny operator
in experiments). Then a Hough transform is used to find the center and radius of
the pupil. Finally, the outer boundary will be detected by using edge detection and

626 Z.Yang,Z.Yang&L.Yang
(a) (b)
(c)
Fig. 2. Iris image preprocessing: (a) original image; (b) localized image; (c) normalized image.
Hough transform again in a certain region determined by the center of the pupil.
A localized image is shown in Fig. 2(b).
Irises from different people may be captured in different sizes and, even for
irises from the same eye, the size may change due to illumination variations and
other factors. It is necessary to compensate for the iris deformation to achieve more
accurate recognition results. Here, we counterclockwise unwrap the iris ring to a
rectangular block with a fixed size (64 × 512 in our experiments). 6,14 That is, the
original iris in a Cartesian coordinate system is projected into a doubly dimensionless
pseudopolar coordinate system. The normalization not only reduces to a
certain extent distortion caused by pupil movement but also simplifies subsequent
processing. A normalized image is shown in Fig. 2(c).
3. Feature Extraction and Matching
3.1. The Hilbert–Huang Transform
The Hilbert–Huang Transform (HHT) was proposed by Huang et al., 11 which is
an important method for signal processing. It consists of two parts: the empirical
mode decomposition (EMD) andtheHilbert spectrum. With EMD, any complicated
data set can be decomposed into a finite and often small number of intrinsic mode
functions (IMFs). An IMF is defined as a function satisfying the following two
conditions: (1) it has exactly one zero-crossing between any two consecutive local
extrema; (2) it has zero local mean.

Iris Recognition Based on Hilbert–Huang Transform 627
By the EMD algorithm, any signal x(t) can be decomposed into finite IMFs,
cj(t)(j =1, 2,...,n), and a residue r(t), where n is the number of IMFs, i.e.
x(t) =
n
cj(t)+r(t). (1)
j=1
Having obtained the IMFs by EMD, we can apply the Hilbert transform to each
IMF, cj(t), to produce its analytic signal zj(t) =cj(t) +iH[cj(t)] = aj(t)e iθj(t) .
Therefore, x(t) can also be expressed as
x(t) =Re
n
aj(t)e iθj (t) + r(t). (2)
j=1
Equation (2) enables us to represent the amplitude and the instantaneous frequency
as functions of time in a three-dimensional plot, in which the amplitude is contoured
on the time–frequency plane. The time–frequency distribution of amplitude
is designated as the Hilbert spectrum, denoted by H(f,t) whichgivesatime–
frequency–amplitude distribution of a signal x(t). HHT brings sharp localizations
both in frequency and time domains, so it is very effective for analyzing nonlinear
and nonstationary data.
With the Hilbert spectrum defined, the Hilbert marginal spectrum can be
defined as
h(f) =
T
0
H(f,t)dt. (3)
The Hilbert marginal spectrum offers a measure of total amplitude (or energy)
contribution from each frequency component.
3.2. Main frequency and main frequency center
It is found that the Hilbert marginal spectrum h(f) has some properties, which can
be used to extract features for iris recognition. Specifically, the main frequency center
of the Hilbert marginal spectrum can be served as a feature to identify different
irises. The “main frequency” and “main frequency center” concepts proposed by us
have been clear described and discussed in our previous works. 26,27 We have shown
that the main frequency center can characterize the approximate period very well.
Here, we only review the definitions of main frequency, main frequency center and
other related concepts as follows.
Definition 1 (Main frequency). Let x(t) be an arbitrary time series and h(f)
be its Hilbert marginal spectrum, then fm is called as the main frequency of x(t), if
h(fm) ≥ h(f), ∀f.
Definition 2 (Average Hilbert marginal spectrum of signal series). Let
X = {xj(t)|j =1, 2,...,N}, whereeachxj(t) isatimeseries,andhj(f) bethe

628 Z.Yang,Z.Yang&L.Yang
Hilbert marginal spectrum of xj(t). The average Hilbert marginal spectrum of X
is defined as
H(f) = 1
N
hj(f). (4)
N
j=1
f H m is called as the average main frequency of X if f H m satisfies H(f H m ) ≥ H(f), ∀f.
For a given set of signal series, in which signals are approximately periodic, the
main frequency can characterize the approximate period very well. Unfortunately, in
some cases a signal may not have a unique main frequency. To handle this situation,
all the possible main frequencies have to be considered. Therefore, we can utilize
the gravity frequencies, which is called the “main frequency center”, instead of the
“main frequency”.
Definition 3 (Main frequency center). Let H(fi) (j =1, 2,...,W)bethe
average Hilbert marginal spectrum of X = {xj(t)|j =1, 2,...,N}. Assume H(fi)
is monotone decreasing respect to i. The main frequency center of X is defined as
fC(X) =
M
i=1 fiH(fi)
M
i=1
H(fi) , (5)
where M is the minimum integer satisfying M i=1 H(fi) ≥ P W i=1 H(fi), and 0 <
P < 1 is a given constant. Then e =(1/M ) M i=1 H(fi) is called the energy of
fC(X).
As can be seen from its definition, the main frequency center is the weighted
mean of several frequencies whose Hilbert marginal spectrums are largest. There
and the main frequency center
is a gap between the average main frequency f H m
fC, but the main frequency center will be a steadier recognition feature. Therefore
the main frequency center fC is used instead of the average main frequency f H m to
characterize the approximate period of signal series.
3.3. Iris feature extraction
Although all normalized iris templates have the same size, eyelashes and eyelids
may still appear on the templates and degrade recognition performance. We find
that the upper portion of a normalized iris image (corresponding to regions closer to
the pupil) provides the most useful information for recognition (see Fig. 3). Therefore,
the region of interest (ROI) is selected to remove the influence of eyelashes
and eyelids. That is, the features are extracted only from the upper 75% section
(48 × 512) that is closer to the pupil in our experiments (see Fig. 3). It is known
that an iris has a particularly interesting structure and provides abundant texture
information. Furthermore if we vertically divide the ROI of a normalized image into
three subregions as shown in Fig. 3, the texture information in the subregion will
be more distinct.

ROI {
Iris Recognition Based on Hilbert–Huang Transform 629
Fig. 3. The normalized iris image is vertically divided into four subregions. The three subregions
1,2and3aretheROI.
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Fig. 4. Left, the 11th line signal of the normalized iris image in Fig. 3 along the horizontal
direction. Right, the EMD decomposition result of the 11th line signal.
An iris consists of some basic elements which are similar each other and interlaced
each other. Hence, an iris image is generally periodic to some extent along
some directions, that is, some approximate periods are embed in the iris image. As
an example, let us observe the 11th line signal of the normalized iris image in Fig. 3
along the horizontal direction, as show in the left of Fig. 4. It can be seen that most
of the durations of the waves are similar, i.e. some main frequencies embed in the
signal. As we know, the EMD can extract the low-frequency oscillations very well. 11
With EMD, the decomposition result of the 11th line signal is shown in the right of
Fig. 4. It can be seen that two main approximate periods are extracted in the third
and fourth IMFs. To show it clearly, we plot the original signal (solid line) and the
third IMF (dash line) together in the interval [320, 450] in the left of Fig. 5. It can
be seen that this IMF characterizes the proximate period of the waveform quite well
and the period is about 15 (i.e. the frequency is about 1/15 ≈ 0.067). Similarly, we
plot the original signal (solid line) and the fourth IMF (dash line) together in the
interval [320, 450] in the right of Fig. 5. It can be seen that this IMF characterizes
the proximate period and the variety of the amplitude. This period is about 26 (i.e.
the frequency is about 1/26 ≈ 0.0385).
According to Eq. (3), we can compute the Hilbert marginal spectrum of the
11th line signal of the normalized iris image in Fig. 3, as shown in the left of
Fig. 6. It is evident that the two main frequencies can be extracted from the Hilbert
marginal spectrum correctly. Based on lots of experiments and analysis we found

630 Z.Yang,Z.Yang&L.Yang
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Fig. 6. Left, the Hilbert marginal spectrum of the 11th line signal of the normalized iris in Fig. 3.
Middle, the Hilbert marginal spectrum of the 12th line signal. Right, the average Hilbert marginal
spectrum and the main frequency center fC of the line signal series in the first subregion of the
normalized iris in Fig. 3.
that the main frequency information of signals along the same direction in the same
subregion of an iris is similar. As an example, we compute the Hilbert marginal
spectrum of the 12th line signal of the normalized iris image in Fig. 3, as shown in
the middle of Fig. 6. It can be seen that the Hilbert marginal spectrums of the 12th
signal is very similar with that of the 11th signal. Then we compute the average
Hilbert marginal spectrum of the signal series along the horizontal direction in the
first subregion of Fig. 3, as shown in the right of Fig. 6. It can be seen that it is
not only coincident with the Hilbert marginal spectrum of each line but also more
concentrated. Therefore, based on the average Hilbert marginal spectrum of the
line signal series in each subregion, we can obtain the main frequency center fC
described as Eq. (5) as a reliable feature of the iris.
Since the orientation information is a very important pattern in an iris, 14,24
the main frequency center along the horizontal direction is not only enough to
characterize its texture information. To characterize the orientation information,
the features along the other directions should be considered. First of all, we should

α ( ) α
Iris Recognition Based on Hilbert–Huang Transform 631
Fig. 7. The generation of the signal along angle α of each subregion: choose one point of the first
column and connect all the dotted lines.
present the generation of signal series along angle α of each subregion of an iris.
The generation method can be simply described as follows. As shown in Fig. 7, the
rectangle frame denotes one of the subregion of an iris. Firstly choose one point of
the first column and connect all the dotted lines. Then we obtain one signal along
angle α of the subregion. Similarly, we can generate all the signal series (totally
16 signals) along angle α in the subregion. In experiments, we totally choose 18
directions: 0 ◦ , 10 ◦ ,...,170 ◦ .
It is found that it has a good classification performance when the main frequency
centers described as Eq. (5) are used as features for iris recognition. The features
can cluster the samples of same class of iris. As an example, we show three samples
of the same iris and their main frequency centers of 18 directions in I1 in Fig. 8. It
can be seen that the features cluster very well. Furthermore, the gaps are usually
existent for the samples from different classes of iris images. This implies that the
selected features have really a good classification ability for the iris images.
It is also found that the energy e of the main frequency center is also a good
feature for classification. It can reflect the image contrast of different classes of iris.
The higher the contrast is, the larger energy the image has. In other words, a signal
will have a larger energy if it waves in a larger amplitude. Thus, a larger energy
in marginal spectrum can be expected if an iris has the higher contrast. It can be
seen from Fig. 9 that in these three iris classes (a), (b) and (c), the class (a) has
the highest contrast while the class (c) has the lowest contrast. It indicates that the
class (a) has generally the largest energy while the class (c) has the smallest energy
of the main frequency center along the same orientation. An encouraging result is
received as shown in Fig. 9(d). It implies that the energies of the main frequency
center should be also used as features to classify the irises.
As is known, that we choose the main frequency center and its energy as features,
now the feature extraction algorithm is presented as follows.
Algorithm 1 (Feature extraction algorithm). Given a normalized iris image
I(i, j), let its three subregions from the top down divided as Fig. 3 be I1, I2
and I3.
D = {di|di =(i − 1)10,i=1, 2,...,18} — the feature orientations.
. . . . . .

632 Z.Yang,Z.Yang&L.Yang
Main Frequency Center
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(a) (b) (c)
0 20 40 60 80
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100 120 140 160
(d)
Fig. 8. (a)–(c) are three samples of the same iris; (d) their main frequency centers of 18 orientations
in I1.
Step 1: Calculate the main frequency centers and energies of 18 orientations of
I1 to form the main frequency vector, f1, by the following six steps.
(1) Let i =1.
(2) Generate 16 signals along orientation di as described in Fig. 7 to form
the signal set, denoted by X.
(3) Calculate the average Hilbert marginal spectrum of X.
(4) Calculate the main frequency center fC(I1(di)) and its corresponding
energy e(I1(di)) of X.
(5) Let i = i +1, if i ≤ 18, then go back to (2); otherwise go to (6).
(6) Obtain the main frequency vector f1 as follows
f1 =(fC(I1(0)),...,fC(I1(170)),e(I1(0)),...,e(I1(170))).
(a)
(b)
(c)

Energy
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Iris Recognition Based on Hilbert–Huang Transform 633
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0 20 40 60 80 100 120 140 160
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(d)
Fig. 9. (a)–(c) are three samples from three different iris classes; (d) each class contains three
samples. The energies of the main frequency center of 18 orientations in I1.
Step 2: Calculate the main frequency centers and its energies of 18 orientations of
I2 similarly to form the main frequency vector
f2 =(fC(I2(0)),...,fC(I2(170)),e(I2(0)),...,e(I2(170))).
Step 3: Calculate the main frequency centers and its energies of 18 orientations of
I3 similarly to form the main frequency vector
f3 =(fC(I3(0)),...,fC(I3(170)),e(I3(0)),...,e(I3(170))).
Step 4: Finally the feature vector of the iris is defined as
The feature vector contains 108 components.
F =(f1,f2,f3).
(a)
(b)
(c)

634 Z.Yang,Z.Yang&L.Yang
The proposed iris feature vector has nice properties. Let us discuss its invariance
and the robustness to noise as follows.
3.3.1. Invariance
It is desirable to obtain an iris representation invariant to translation, scale, rotation
and illumination. In our method, translation invariance and approximate scale
invariance are achieved by normalizing the original image at the preprocessing step.
Rotation invariance is important for an iris representation since changes of head
orientation and binocular vergence may cause eye rotation. Most existing schemes
achieve approximate rotation invariance either by rotating the feature vector before
matching4,6,7,15,23 or by defining several templates which denote other rotation
angles for each iris class in the database. 5,14 In our algorithm, the annular iris is
unwrapped into a rectangular image. Therefore, rotation in the original image just
corresponds to translation in the normalized image (for example, clockwise rotation
of 90◦ in the original image just corresponds to circle translation 128 pixels towards
the left side in the normalized image, as shown in Figs. 10(a)–(d)). Fortunately,
translation invariance can easily be achieved in our method. Since translation in
the original signal will just result in almost the same translation of all IMFs and
the residue, 11 as shown in Fig. 10(e), (f). Furthermore, if let g(t) =g(t − t0), we
have
H[g](t) = 1
π p.v.
∞
g(t
−∞
′ )
t − t ′ dt′ = 1
π p.v.
∞
g(t
−∞
′ )
(t − t0) − t ′ dt′ = H[g](t − t0).
Therefore, translation in the IMFs just results in the same translation in its Hilbert
transform so as its instantaneous frequencies. Then the Hilbert marginal spectrums
of the original signal and the translation signal will be the same. Finally, the main
frequency center and its energy based on the average Hilbert marginal spectrum of
signal series will also keep the same. Additionally, we can also observe this property
intuitively. Since our feature is based on the vertical subregion of the normalized
image, translation in the normalized image will not change the information of the
subregion. Therefore, the feature will keep the same.
Since the illuminations of iris images may be different caused by the position
of light sources, the feature invariant to illumination will be also important. To
investigate the effect of illumination, let us consider two iris images from the same
iris image with different illuminations shown in Figs. 11(a) and 11(b). As can be
seen from their EMD decomposition results in Figs. 11(c) and 11(d), their difference
is mainly on the residues. The residue of Fig. 11(c) is about 190, while the residue
of Fig. 11(d) is about 130. As we know the residue of EMD is removed before
computing the Hilbert marginal spectrum, so the illumination variation will not
influence the main frequency center and its energy. If we remove the residues of
all lines from the original images, the residual images of Figs. 11(a) and 11(b)
are shown in Figs. 11(e) and 11(f), respectively. It can be seen that it not only
compensates for the nonuniform illumination but also improves the contrast of the

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Iris Recognition Based on Hilbert–Huang Transform 635
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Fig. 10. (a) Original image; (b) the image after rotating 90 ◦ clockwise; (c) the normalized image
of the original image; (d) the normalized image of the rotated image; (e) the EMD decomposition
result for the 10th line along horizon of the original normalized image; (f) the EMD decomposition
result for the 10th line along horizon of the rotated normalized image.
image. Therefore other than most of other iris recognition methods, our method
need not do the enhancement processing in the iris image preprocessing.
3.3.2. Robustness to noise
Just as stated in Refs. 3, 11 and 26 the high frequency noise is mainly contained in
the first IMF. Moreover, it is found that the first IMF is not a significant component
to characterize the iris structure. To be robust to high frequency noise, the first IMF
is removed when the Hilbert marginal spectrum is calculated in our method. Though
it leads a slight change for the main frequency, it can relieve the high frequency
noises.
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636 Z.Yang,Z.Yang&L.Yang
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(c) (d)
(e) (f)
Fig. 11. (a) Iris image with bright illumination; (b) the same iris image with dark illumination;
(c) the EMD decomposition result of the 10th line of (a); (d) the EMD decomposition result of
the 10th line of (b); (e) the result by removing all the residues of lines from (a); (f) the result by
removing all the residues of lines from (b).
To show the robustness of our method to noise, we added 20 dB Gauss white
noise to the iris image as shown in Fig. 12(a) and calculate the main frequency
centers and the energies of 18 orientations in I1 of the original normalized image
and the noise normalized image, as shown in Figs. 12(b) and 12(c), respectively.
It can be seen that most features of the noisy iris image just have small changes
compared with those of the original iris. Therefore, the proposed feature is robust
to high frequency noise.
3.4. Iris matching
After feature extraction, an iris image is represented as a feature vector of length
108. To improve computational efficiency and classification accuracy, Linear Discriminant
Analysis (LDA) is first used to reduce the dimensionality of the feature
vector and then the Euclidean similarity measure is adopted for classification. LDA
is a linear statistic classification method, which intends to find a linear transform T
as such that, after its application, the scatter of sample vectors is minimized within
each class, and the scatter of those mean vectors around the total mean vector can
be maximized simultaneously. Further details of LDA may be found in Ref. 8.

Main Frequency Center
0.06
0.05
0.04
0.03
0.02
0 20 40 60 80
Orientation
100 120 140 160
Iris Recognition Based on Hilbert–Huang Transform 637
Original features
Noise features
(a)
Energy
500
400
300
200
Original features
Noise features
0 20 40 60 80
Orientation
100 120 140 160
(b) (c)
Fig. 12. (a) The original iris image; (b) the main frequency centers of 18 orientations in I1 of the
original normalized image (“o”) and those of the noisy normalized image (“•”); (c) the energies
of 18 orientations in I1 of the original normalized image (“o”) and those of the noisy normalized
image (“•”).
4. Experimental Results
To evaluate the performance of the proposed method, we applied it to the widely
used database named CASIA iris database. 1 The database includes 2255 iris images
from 306 different eyes (hence, 306 different classes). The captured iris images are
8-bit gray images with a resolution of 320 × 280.
4.1. Performance of the proposed method
For each iris class, we choose three samples taken at the first session for training and
all samples captured at the second and third sessions serve as test samples. Therefore,
there are 918 images for training and 1337 images for testing. Figure 13(a)
describes variations of the correct recognition rate (CRR) with changes of dimensionality
of the reduced feature vector using the LDA. From this figure, we can see
that with increasing dimensionality of the reduced feature vector, the recognition
rate also increases rapidly. However, when the dimensionality of the reduced feature

638 Z.Yang,Z.Yang&L.Yang
Correct recognition rate
100
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99
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10 20 30 40 50 60 70 80 90
Dimensionality of the feature vector
Density (£¥)
40
35
30
25
20
15
10
5
intra-class distribution
inter-class distribution
0
0 5 10 15 20 25 30 35 40
Normalized matching distance
(a) (b)
Fig. 13. (a) Recognition results using features of different dimensionality using LDA. (b) Distributions
of intra- and inter-class distances.
vector is up to 70 or higher, the recognition rate starts to level off at an encouraging
CRR of about 99.4%. In the experiments, we utilize the Euclidian similarity
measure for matching. The results indicate that the proposed method will be highly
feasible in practical applications.
To evaluate the performance of the proposed method in verification mode,
each tested iris image is compared with all the trained iris images on the CASIA
database. Therefore, the total number of comparisons is 1337 × 918 = 1,227,366,
where the total number of intra-class comparisons is 1337 × 3 = 4011, and that
of inter-class comparisons is 1337 × 915 = 1,223,355. Figure 13(b) shows distributions
of intra- and inter-class matching distances on the CASIA iris database.
As shown in Fig. 13(b), we can find that the distance between the intra- and the
inter-class distributions is large, and the portion that overlaps between the intraand
the inter-class is very small. This proves that the proposed features are highly
discriminating.
In verification mode, the receiver operating characteristic (ROC) curve and
equal error rate (EER) are used to evaluate the performance of the proposed
method. 17 The ROC curve is a false accept rate (FAR) versus false reject rate
(FRR) curve, which measures the accuracy of matching process and shows the
overall performance of an algorithm. Points on this curve denote all possible system
operating states in different tradeoffs. The EER is the point where the FAR
and the FRR are equal in value. The smaller the EER is, the better the algorithm
is. Figure 14(a) shows the ROC curve of the proposed method on the CASIA iris
databases. It can be seen that the performance of our algorithm is very high and
the EER is only 0.27%. If we choose the threshold as 17.2, the CRR is up to 99.7%
when the FRR is less than 0.15%.

False Reject Rate(%)
0
2.5
2
1.5
1
0.5
0.1 0.2 0.3
False Accept Rate(%)
0.4 0.5
Iris Recognition Based on Hilbert–Huang Transform 639
Correct recognition rate
100
90
80
70
60
50
40
30
20
10
0
40dB 30dB 20dB
Signal−to−noise ratio
10dB
(a) (b)
Fig. 14. (a) The ROC curve of our method on CASIA iris database. (b) Recognition results of
adding different SNR to the tested iris images.
As discussed in the above section, our method is robust to high frequency noise.
To evaluate the robustness of our method to noise, we added Gauss white noise with
different signal-to-noise ratio (SNR) to the test iris images. The result is shown in
Fig. 14(b). The result is encouraging, since the correct recognition rates are 97.2%,
95.6%, 92.2% and 87.5%, respectively, when SNR = 40, 30, 20 and 10 dB.
4.2. Comparison with existing methods
Among existing methods for iris recognition, those proposed by Daugman, 7 Wildes
et al., 4 and Tan et al., 14,15 respectively, are the best known. Furthermore, they
characterize the iris from different viewpoints. To further prove the effectiveness
of our method, we make comparison with the above four methods on the CASIA
iris database. The experimental results are shown in the Table 1. It can be seen
that the performance of our method is encouraging and comparable to the best
iris recognition algorithm while the dimension of our feature vector is very low.
Furthermore, as discussed above our method is rotation-invariant and illuminationinvariant.
Besides it is robust to high frequency noise.
Table 1. The feature dimension and correct recognition rate comparisons
of several well-known methods.
Methods Feature dimension Correct recognition rate (%)
Boles and Boashash 4 1024 92.4
Daugman 7 2048 100
Tan and co-workers 15 660 99.6
Tan and co-workers 14 1536 99.43
Our method 108 99.4

640 Z.Yang,Z.Yang&L.Yang
5. Conclusions
Recently, iris recognition has received increasing attention for human identification
due to its high reliability. HHT is an analysis method for nonlinear and
nonstationary data. In this paper, we have presented an efficient iris recognition
method based on HHT by extracting the main frequency center information. This
new method benefits a lot: firstly, its dimension of feature vector is very low compared
with the other famous methods; secondly, other than most of other iris
recognition methods, our method need not do the enhancement processing in the
iris image preprocessing and is illumination-invariant; thirdly, unlike most existing
methods to achieve approximate rotation invariance by defining several templates
denoting other angles, our method is really rotation-invariant; fourthly, it is robust
to high frequency noise; Moreover, the experimental results on the CASIA iris
database show that the correct recognition rate of the proposed method is encouraging
and comparable to the best iris recognition algorithm. In addition, the proposed
method has demonstrated that HHT is a powerful tool for feature extraction
and will be useful for many other pattern recognitions.
Acknowledgments
Portions of the research in this paper use the CASIA iris image database collected
by Institute of Automation, Chinese Academy of Sciences.
This work is supported by NSFC (Nos. 10631080, 60873088, 60475042), and
NSFGD (No. 9451027501002552).
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